In general, as long as you can satisfy all conservation laws, you can get matter from pure radiation. Weinberg's 'First three minutes' has a good light-weight(ish) treatment of nucleosynthesis during the early stages of Big Bang, which included matter creation.

Both of nuclear fission reactions and fusion reactions result in the creation of new atoms, although of course these are produced from previously existing atoms.
The very first atoms, nearly all Hydrogen and Helium, came in to being several hundred thousands of years after the big bang.
Before that the Universe was a very hot plasma of particles, too hot for electrons to bind with protons.
After that the first generation of stars came in to being, these fusing the H and He into bigger atoms - other elements.